1. Trim log files

This will truncate any *.log files on the volume /var that are either older than 7 days and greater than 50M or older than 30 days.

2. Cleanup YUM cache

The simple command to cleanup yum caches:

yum clean all

Note that the above command will not remove everything related to yum.
You may want to free up space taken by orphaned data from disabled or removed repositories:

rm -rf /var/cache/yum

Also, when you accidentally run yum through a regular user (forgot sudo), yum will create user-cache. So let’s delete that too:

rm -rf /var/tmp/yum-*

3. Remove orphan packages

Check existing orphan packages

package-cleanup --quiet --leaves --exclude-bin

Confirm removing orphan packages

Now, if happy with suggestions given by the previous command, run:

package-cleanup --quiet --leaves --exclude-bin | xargs yum remove -y

4. Remove WP CLI cached WordPress downloads

WP CLI saves WordPress archives every time you setup a new WordPress website. You can remove those caches by the following command:

rm -rf /root/.wp-cli/cache/*
rm -rf /home/*/.wp-cli/cache/*

5. Remove old kernels

The following command will keep just 2 latest kernels installed:

package-cleanup --oldkernels --count=2

Note that with some VPS providers (Linode for example), servers use provider’s built kernels by default and not the ones on the server itself. So it makes little sense to keep more than 1 old kernel on the system. So:

package-cleanup --oldkernels --count=1

6. Remove Composer cache

rm -rf /root/.composer/cache
rm -rf /home/*/.composer/cache

7. Remove core dumps

If you had some severe failures with PHP which caused it to segfault and had core dumps enabled, chances are – you have quite a few of those.
They are not needed after you done debugging the problem. So:

find -regex ".*/core\.[0-9]+$" -delete

8. Remove error_log files (cPanel)

If you use the disgusting cPanel, you surely got dozens of error_log files scattered across your web directories. Much better if you can install the Citrus Stack. A temporary solution is to remove all those files: